Question

Find the angle between the vectors u=3i+j and v=-2i+4j

Answer 1

\[u.v=\left| u \right|\left| v \right|\cos \theta \]
where theta is the angle between u and v.

Answer 2

\[uxv=\left| u \right|\left| v \right|\cos (\theta)\]
\[\left| u \right|=\sqrt{10}\]
\[\left| v \right|=\sqrt{50}\ \]

Answer 3

yes i used that formula too but not sure about the answer i got 98.1 degree

Answer 4

is there a way to check if the angle is in the right quadrant?

Answer 5

\[\left| v \right|=\sqrt{\left( -2 \right)^2+\left( 4 \right)^2}=\sqrt{20}\]

Answer 6

\[u.v=(3)(-2)+(1)(4)=-6+4=-2\]
\[-2=\sqrt{10}\sqrt{20}\cos \theta =10\sqrt{2}\cos \theta ,\cos \theta=\frac{ -\sqrt{2} }{ 10 }\]
98.1 is correct.